In the case you're asking about, I would use bias binding. It just makes it easier to get the corners how you want them.
Re pressing the binding before sewing - I used to, but a couple of years ago I read that it is easier to get it to lay nicely if you don't press first. Tried that, liked it and never went back to pressing before sewing.
Good luck with however you choose to proceed.

When you say "Don't press first", do you mean that you don't press it in half?
I plan to do a 2 1/4" binding that I would normally then press in half.

Watson